Chapter MPS, Problem 11.10MPS

To determine

Expression for the volume of cube.

Answer to Problem 11.10MPS

Expression for the volume of cube = $27x^3+54x^2+44$

Explanation of Solution

Given information:

Side of cube = $3x+2$

Formula used:

Volume of cube = $a^3$

Where $a$ is the side of the cube.

  ${\left(a+b\right)}^3=a^3+b^3+3ab\left(a+b\right)$

Side of the cube = $3x+2$

Now finding the volume of the cube using formula $a^3$ , here $a$ is the side of cube.

  $\begin{array}{l}volume={\left(side\right)}^3\\ volume={\left(3x+2\right)}^3\end{array}$

Now applying ${\left(a+b\right)}^3$ identity:

  $\begin{array}{l}volume={\left(3x\right)}^3+{\left(2\right)}^3+3\left(3x\right)\left(2\right)\left(3x+2\right)\\ volume=27x^3+8+54x^2+36\\ \boxed{volume=27x^3+54x^2+44}\end{array}$

Expression for the volume of cube = $27x^3+54x^2+44$